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Math Help - Did I answer these questions correctly?

  1. #1
    TWN
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    Did I answer these questions correctly?

    1.) Convert the rectangular equation x^2 + y^2 - 2ax = 0 to its polar equivalent.

    My answer is r = sqrt(2ax)

    Not confident that one's right.

    2.) Convert the rectangular equation xy = 4 to its polar equivalent.

    My answer is (r^2)sin(theta)cos(theta) = 4

    Not sure if that's a complete answer.

    3.) Convert the rectangular equation (x^2 + y^2)^2 - 9(x^2 + y^2) to its polar equivalent.

    My answer: r = 0

    The way I got that answer seemed waaaay too easy.

    4.) Convert polar equation r = cot(theta)csc(theta) to its rectangular equivalent.

    My answer is x = y^2

    I'm pretty confident about that one.



    Please look over what I've done and let me know if any of my answers are wrong. If one is wrong, please explain how to reach the correct answer.

    Thank you in advance!
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  2. #2
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    Re: Did I answer these questions correctly?

    Quote Originally Posted by TWN View Post
    1.) Convert the rectangular equation x^2 + y^2 - 2ax = 0 to its polar equivalent.

    My answer is r = sqrt(2ax)

    Not confident that one's right.

    2.) Convert the rectangular equation xy = 4 to its polar equivalent.

    My answer is (r^2)sin(theta)cos(theta) = 4

    Not sure if that's a complete answer.

    3.) Convert the rectangular equation (x^2 + y^2)^2 - 9(x^2 + y^2) to its polar equivalent.

    My answer: r = 0

    The way I got that answer seemed waaaay too easy.

    4.) Convert polar equation r = cot(theta)csc(theta) to its rectangular equivalent.

    My answer is x = y^2

    I'm pretty confident about that one.


    Please look over what I've done and let me know if any of my answers are wrong. If one is wrong, please explain how to reach the correct answer.

    Thank you in advance!
    I disagree with Q1. Your final answer should NOT have any x's or y's left in it.

    Q2 seems fine.

    Q3 is not an equation.

    Q4 seems fine.
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  3. #3
    TWN
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    Re: Did I answer these questions correctly?

    What is the correct way to approach 1 and 3, please?
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  4. #4
    TWN
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    Re: Did I answer these questions correctly?

    Oh wow, 3 is way easier than I first made it out to be. r = 3, correct?

    Edit: And for #1, is r = 2a(cos(theta)) correct?
    Last edited by TWN; October 3rd 2012 at 10:08 PM.
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    Re: Did I answer these questions correctly?

    Quote Originally Posted by TWN View Post
    Oh wow, 3 is way easier than I first made it out to be. r = 3, correct?

    Edit: And for #1, is r = 2a(cos(theta)) correct?
    I still disagree with 3. Are you sure you haven't made a typo? I agree with your new answer to 1.
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  6. #6
    TWN
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    Re: Did I answer these questions correctly?

    Ah, I see what you're getting at now. The rectangular equation is (x^2 + y^2)^2 - 9(x^2 + y^2) = 0

    Sorry about that..
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    Re: Did I answer these questions correctly?

    Quote Originally Posted by TWN View Post
    Ah, I see what you're getting at now. The rectangular equation is (x^2 + y^2)^2 - 9(x^2 + y^2) = 0

    Sorry about that..
    OK, so what do you get for the polar form of this equation?
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  8. #8
    TWN
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    Re: Did I answer these questions correctly?

    r = 3

    Is that not right?

    Here are my steps:

    (x^2 + y^2)^2 - 9(x^2 + y^2) = 0

    r^4 - 9r^2 = 0

    r^4 = 9r^2

    r^2 = 9

    r = 3
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    Re: Did I answer these questions correctly?

    Quote Originally Posted by TWN View Post
    r = 3

    Is that not right?

    Here are my steps:

    (x^2 + y^2)^2 - 9(x^2 + y^2) = 0

    r^4 - 9r^2 = 0

    r^4 = 9r^2

    r^2 = 9

    r = 3
    There are more solutions than that. The first fundamental rule is that you may not divide by 0. You need to factorise the equation then set each factor equal to 0.
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